Giampiero Ventura surprised many by setting Toro out in an attacking 4-3-3 formation, as the returning Omar El Kaddouri started wide on the left, with Alessio Cerci in his favoured position on the right wing.
The Granata made a blistering start and were ahead after just four minutes, as Cerci beat Giuseppe Gemiti for pace, before delivering an excellent right footed cross for Ciro Immobile to tap home.
Then moments later, the visitors doubled their lead when a Cerci corner was headed in by captain Kamil Glik, who scored his first goal of the season.
However, Livorno reacted well to that early set back, although it must be said they were assisted in getting back into the match by Torino who continued to give the ball back to the hosts. On the twenty-five minute mark, the home side got a goal back, when Pasquale Schiattarella's low cross was turned in by Paulinho.
And just eight minutes later, Livorno grabbed a deserved equaliser when an excellent dummy from Paulinho attracted three players to him, and that gave Leandro Greco the space to score from the edge of the area.
Torino almost regained the lead just before half time, but home goalkeeper Francesco Bardi made an outstanding save to deny Kamil Glik his second goal of the evening.
In the second half, Livorno almost took the lead for the first time in the match, but Daniele Padelli made an excellent save with his legs to deny striker Innocent Emeghara.
However, the former Udinese goalkeeper could do nothing to prevent defender Emerson from giving his side the lead on the hour mark. The Brazilian defender ran from his own half unleashing an unstoppable left footed shot from 35 yards to leave Padelli stranded.
But Torino showed some character to come back into the match, and they thought they had equalised when substitute Paulo Barreto played in Danilo D'Ambrosio, but the full back could only hit the post. With just minutes remaining, Torino received a lifeline when defender Leandro Rinaudo handled Ciro Immobile's goal bound effort and referee Paolo Valeri pointed to the spot.
Despite missing a penalty in the game against Inter, Alessio Cerci made no mistake on this occasion and he capped an excellent individual performance with a crucial goal. As Italian football pundit James Horncastle pointed out, Torino certainly aren't boring this season, but if they are to improve on last season's finish of 16th, they will have to learn to defend much better.
However, thankfully Torino have a nice easy game at the weekend - as league leaders Roma, who have won nine games out of nine, and conceded just one goal come to the Stadio Olimpico.